- #1
climbon
- 18
- 0
I have an equation that I am trying to change the variables of, it has the form;
[tex]
\frac{d}{dt} W = g \frac{\partial}{\partial y} U + h x \frac{\partial^2}{\partial y^2} Z
[/tex]
Where W, U and Z are my dependent variables (This equation is just one of 3 coupled equations but have written only the above in general form).
I want to change the variables into a rotating frame, so;
x -----> x' = x(0) cos(wt) + y(0) sin(wt)
y -----> y' = -x(0) sin(wt) + y(0) cos(wt)
When putting these into the top equation, obviously it is simple to replace the x and y's but how do I change the differentials w.r.t. y with the new variable?
Thanks for any help :D
[tex]
\frac{d}{dt} W = g \frac{\partial}{\partial y} U + h x \frac{\partial^2}{\partial y^2} Z
[/tex]
Where W, U and Z are my dependent variables (This equation is just one of 3 coupled equations but have written only the above in general form).
I want to change the variables into a rotating frame, so;
x -----> x' = x(0) cos(wt) + y(0) sin(wt)
y -----> y' = -x(0) sin(wt) + y(0) cos(wt)
When putting these into the top equation, obviously it is simple to replace the x and y's but how do I change the differentials w.r.t. y with the new variable?
Thanks for any help :D